51. 
 Andreasson, Håkan, 1966, et al.
(författare)

Proof of the cosmic nohair conjecture in the T3Gowdy symmetric EinsteinVlasov setting
 2016

Ingår i: Journal of the European Mathematical Society.  14359855 . 14359863. ; 18:7, s. 15651650

Tidskriftsartikel (refereegranskat)abstract
 The currently preferred models of the universe undergo accelerated expansion induced by dark energy. One model for dark energy is a positive cosmological constant. It is consequently of interest to study Einstein's equations with a positive cosmological constant coupled to matter satisfying the ordinary energy conditions: the dominant energy condition etc. Due to the difficulty of analysing the behaviour of solutions to Einstein's equations in general, it is common to either study situations with symmetry, or to prove stability results. In the present paper, we do both. In fact, we analyse, in detail, the future asymptotic behaviour of T3Gowdy symmetric solutions to the EinsteinVlasov equations with a positive cosmological constant. In particular, we prove the cosmic nohair conjecture in this setting. However, we also prove that the solutions are future stable (in the class of all solutions). Some of the results hold in a more general setting. In fact, we obtain conclusions concerning the causal structure of T2symmetric solutions, assuming only the presence of a positive cosmological constant, matter satisfying various energy conditions and future global existence. Adding the assumption of T3Gowdy symmetry to this list of requirements, we obtain C0estimates for all but one of the metric components. There is consequently reason to expect that many of the results presented in this paper can be generalised to other types of matter.


52. 


53. 
 Andréasson, Håkan
(författare)

Pseudomyxoma Peritonei : Aspects of Natural History, Learning Curve, Treatment Outcome and Prognostic Factors
 2013

Doktorsavhandling (övrigt vetenskapligt)abstract
 Pseudomyxoma peritonei (PMP) is a rare disease characterized by mucinous peritoneal metastasis (PM). Different locoregional treatment strategies, i.e. debulking surgery and cytoreductive surgery (CRS) in combination with hyperthermic intraperitoneal chemotherapy (HIPEC), have changed the prognosis for these patients. CRS is an aggressive surgical procedure with a long learning curve. PMP exists in different types; how many depends on which classification is used.The aims of this thesis were to investigate the timeframe of PMP development from an isolated appendiceal neoplasm, examine the learning process for CRS, evaluate the differences in treatment outcome between debulking surgery and CRS in combination with HIPEC, to evaluate a more detailed PMP classification and to investigate particularly interesting new cysteinehistidine (PINCH) protein as a prognostic factor for PMP.Retrospectively 26 PMP patients were identified as having had an appendectomy with a neoplasm in the appendix but with no evidence of PM at the appendectomy. They were treated for PMP within a median of 13.1 months (3.895.3) after the appendectomy. No difference was seen between the types of PMP regarding the time to a clinically significant development of PMP and how much tumour was found at treatment. CRS is a highly invasive treatment and stabilization in the learning curve was seen after 220±10 procedures. Patients treated with CRS+HIPEC had a better 5year overall survival (OS) than patients treated with debulking surgery, 74% vs. 40%. CRS increased the rate of complete cytoreduction from 25% in patients treated with debulking surgery to 72%. The new fourgrade PMP classification showed very good interrater agreement between two independent pathologists and a difference in survival rates was observed between the different grades. A positive PINCH staining was recorded in 83% of the tumours and that was associated with poorer survival.


54. 
 Andreasson, Håkan, 1966
(författare)

Regularity Results for the Spherically Symmetric EinsteinVlasov System
 2010

Ingår i: Annales Henri Poincare.  14240637 . 14240661. ; 11:5, s. 781803

Tidskriftsartikel (refereegranskat)abstract
 The spherically symmetric EinsteinVlasov system is considered in Schwarzschild coordinates and in maximalisotropic coordinates. An open problem is the issue of global existence for initial data without size restrictions. The main purpose of the present work is to propose a method of approach for general initial data, which improves the regularity of the terms that need to be estimated compared to previous methods. We prove that global existence holds outside the center in both these coordinate systems. In the Schwarzschild case we improve the bound on the momentum support obtained in Rein et al. (Commun Math Phys 168:467478, 1995) for compact initial data. The improvement implies that we can admit noncompact data with both ingoing and outgoing matter. This extends one of the results in Andreasson and Rein (Math Proc Camb Phil Soc 149:173188, 2010). In particular our method avoids the difficult task of treating the pointwise matter terms. Furthermore, we show that singularities never form in Schwarzschild time for ingoing matter as long as 3m <= r. This removes an additional assumption made in Andreasson (Indiana Univ Math J 56:523552, 2007). Our result in maximalisotropic coordinates is analogous to the result in Rendall (Banach Center Publ 41:3568, 1997), but our method is different and it improves the regularity of the terms that need to be estimated for proving global existence in general.


55. 


56. 
 Andreasson, Håkan, 1966, et al.
(författare)

Rotating, Stationary, Axially Symmetric Spacetimes with Collisionless Matter
 2014

Ingår i: Communications in Mathematical Physics.  00103616 . 14320916. ; 329:2, s. 787808

Tidskriftsartikel (refereegranskat)abstract
 The existence of stationary solutions to the Einstein–Vlasov system which are axially symmetric and have nonzero total angular momentum is shown. This pro vides mathematical models for rotating, general relativistic and asymptotically flat non vacuum spacetimes. If angular momentum is allowed to be nonzero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on R 5.


57. 


58. 
 Andreasson, Håkan, 1966
(författare)

Sharp bounds on 2m/r of general spherically symmetric static objects
 2008

Ingår i: Journal of Differential Equations.  10902732 . 00220396. ; 245:8, s. 22432266

Tidskriftsartikel (refereegranskat)abstract
 In 1959 Buchdahl [H.A. Buchdahl, General relativistic fluid spheres, Phys. Rev. 116 (1959) 10271034] obtained the inequality 2 M / R ≤ 8 / 9 under the assumptions that the energy density is nonincreasing outwards and that the pressure is isotropic. Here M is the ADM mass and R the area radius of the boundary of the static body. The assumptions used to derive the Buchdahl inequality are very restrictive and for instance neither of them hold in a simple soap bubble. In this work we remove both of these assumptions and consider any static solution of the spherically symmetric Einstein equations for which the energy density ρ ≥ 0, and the radial and tangential pressures p ≥ 0 and pT satisfy p + 2 pT ≤ Ω ρ, Ω > 0, and we show thatunder(sup, r > 0) frac(2 m (r), r) ≤ frac((1 + 2 Ω)2  1, (1 + 2 Ω)2), where m is the quasilocal mass, so that in particular M = m (R). We also show that the inequality is sharp under these assumptions. Note that when Ω = 1 the original bound by Buchdahl is recovered. The assumptions on the matter model are very general and in particular any model with p ≥ 0 which satisfies the dominant energy condition satisfies the hypotheses with Ω = 3.


59. 


60. 
 Andreasson, Håkan, 1966
(författare)

Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres
 2009

Ingår i: COMMUNICATIONS IN MATHEMATICAL PHYSICS.  00103616 . 14320916. ; 288:2, s. 715730

Tidskriftsartikel (refereegranskat)abstract
 In a recent paper by Giuliani and Rothman [17], the problem of finding a lower bound on the radius R of a charged sphere with mass M and charge Q < M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M ≤ 4R/9, has been found. In this paper we derive the surprisingly transparent inequality √M≤/√R3+√/R9+/Q23R. The inequality is shown to hold for any solution which satisfies p + 2pT ≤ ρ, where p ≥ 0 and pT are the radial and tangential pressures respectively and ρ ≥ 0 is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.

